A245715 Least number k > 0 such that n - k! is prime, or 0 if no such k exists.

0, 0, 1, 1, 2, 1, 2, 1, 2, 0, 3, 1, 2, 1, 2, 0, 3, 1, 2, 1, 2, 0, 3, 1, 2, 4, 4, 0, 3, 1, 2, 1, 2, 0, 3, 0, 3, 1, 2, 0, 4, 1, 2, 1, 2, 0, 3, 1, 2, 0, 0, 0, 3, 1, 2, 0, 0, 0, 3, 1, 2, 1, 2, 0, 3, 0, 3, 1, 2, 0, 4, 1, 2, 1, 2, 0, 3, 0, 3, 1, 2, 0, 4, 1, 2, 0, 0, 0, 3, 1, 2, 0, 0, 0, 3, 0, 4, 1, 2, 0, 0, 1, 2, 1, 2, 0, 3, 1, 2, 1, 2, 0, 3, 1, 2, 0, 0, 0, 3

Offset: 1

Author

Derek Orr, Jul 30 2014

Keywords

• nonn

Comments

a(n)! < n for all n. Thus a(n) = 0 is definite.

Examples

			11 - 1! = 10 is not prime.
11 - 2! = 9 is not prime.
11 - 3! = 5 is prime. Thus a(11) = 3.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Programs

PARI

a(n)=for(k=1,n,if(ispseudoprime(n-k!),return(k)))
vector(150,n,a(n))